BMST Algebraic Equations and Inequalities 3 — Questions and Answers
Question 1: A number increased by 8 equals 23. What is the number?
- 31
- 15 (Correct answer)
- 184
- 3
Correct answer: 15
The equation n + 8 = 23 gives n = 15 when you subtract 8 from both sides.
Question 2: Solve for a: 2a + 5 = a - 3
- a = -8 (Correct answer)
- a = 8
- a = 2
- a = -2
Correct answer: a = -8
Subtract a from both sides to get a + 5 = -3, then subtract 5 to get a = -8.
Question 3: What is the solution set for |x| = 6?
- x = 6 only
- x = -6 only
- x = 6 or x = -6 (Correct answer)
- no solution
Correct answer: x = 6 or x = -6
Absolute value equations have two solutions: x = 6 and x = -6, since both have an absolute value of 6.
Question 4: Solve: 3(2x - 1) = 15
- x = 2
- x = 3 (Correct answer)
- x = 4
- x = 6
Correct answer: x = 3
Distribute to get 6x - 3 = 15, add 3 to get 6x = 18, then divide by 6 to get x = 3.
Question 5: On a number line, which description correctly shows x < -2?
- Open circle at -2, shading to the right
- Closed circle at -2, shading to the right
- Open circle at -2, shading to the left (Correct answer)
- Closed circle at -2, shading to the left
Correct answer: Open circle at -2, shading to the left
A strict inequality uses an open circle, and x < -2 means values less than -2, so shading goes left.
Question 6: If 4t - 9 = 3, what is 2t?
- 3
- 6 (Correct answer)
- 9
- 12
Correct answer: 6
Solving gives 4t = 12, so t = 3, and 2t = 6.
Question 7: Which of the following is a solution to the compound inequality -1 < x ≤ 4?
- x = -1
- x = 5
- x = 0 (Correct answer)
- x = -2
Correct answer: x = 0
x = 0 satisfies -1 < 0 ≤ 4; x = -1 is excluded by the strict <, and x = 5 and x = -2 are out of range.
BMST Algebraic Equations and Inequalities 3
A number increased by 8 equals 23.
What is the number?